ITERATIVE METHOD FOR SOLVING A MINIMUM NORM SOLUTION OF SPLIT FEASIBILITY PROBLEM

Abstract

The split feasibility problem is to find a point x ∗ with the property that x ∗ ∈ C and
Ax ∗ ∈ Q, where C and Q are the nonempty closed convex subsets of the real Hilbert spaces H1 and H2, respectively, and A is a bounded linear operator from H1 to H2. In this paper, we propose an iterative method to solve the problem of finding the minimum norm solution of the split feasibility problem in real Hilbert space. We propose a new iterative method, based on the CQ method, to find the extreme value of the distance function on the set of solutions of the split feasibility problem; consider the convergence of the method and give examples of illustrative numbers infinite-dimensional space.